Question

What will be the acceleration due to gravity of an object on a planet whose mass is one-ninth of the mass of the earth and whose radius is half of that of the earth?

Answer 1

Answer:-

Value of acceleration due to gravity on the planet is 4.36m/s² .

Explanation:-

We know that :-

gₑ = GMₑ/R²ₑ -------(1)

Where :-

• gₑ is the mass of earth.

• G is Universal Gravitational Constant.

• Rₑ is the radius of the earth.

Also, value of gₑ i.e. acceleration due to gravity at the surface of earth is 9.8m/s².

Now, according to given condition :-

→ Mass of the planet (Mₚ) = Mₑ/9

→ Radius of the planet (Rₚ) = Rₑ/2

Hence, acceleration due to gravity on that planet (gₚ) will be :-

=> gₚ = GMₚ/R²ₚ

=> gₚ = G×Mₑ/9/[(Rₑ/2)²]

=> gₚ = GMₑ/9/[Rₑ²/4]

=> gₚ = GMₑ/9 × 4/R²ₑ

=> gₚ = 4GMₑ/9R²ₑ -----(2)

On dividing eq.2 by eq.1, we get :-

=> gₚ/gₑ = [4GMₑ/9R²ₑ]/[GMₑ/R²ₑ]

=> gₚ/gₑ = 4/9

=> gₚ = 4×gₑ/9

=> gₚ = 4×9.8/9

=> gₚ = 39.2/9

=> gₚ = 4.36 m/s²